Grosso, who scored the winning penalty for Italy in the shootout win over France at the 2006 World Cup final, began his managerial career in Serie B with Bari and Hellas Verona, before taking charge of Brescia, Sion, Frosinone and Lyon.
His last role came at Sassuolo, where he won promotion in his first campaign, and after guiding them to mid-table safety in Serie A last season, Grosso left the club by mutual agreement on Thursday.
"I never like to make promises," Grosso said in a Fiorentina statement, "but aware of the responsibilities that await me, I immediately feel I can guarantee seriousness, professionalism and involvement in building a team that has courage and ambition."
Fiorentina battled relegation in the most recent campaign, with Stefano Pioli sacked in November after a 10-game winless start. Paolo Vanoli took over and led them to a 15th-place finish, before departing the club on Friday.